I'm reading some PDF in conic programming. When we define duality and want to know when strong duality holds we use Slater's condition. In some references the cone should be pointed and in other pointedness is not needed. Could you please tell me being pointed for the cone is necessary or not?
2026-03-24 20:40:09.1774384809
Slater's condition in conic programming
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There are (at least) two relevant remarks:
Only pointed cones define a partial order.
When a cone is closed, it is pointed if and only if its dual cone has a nonempty interior.